{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we will use Gated Recurrent Unit RNN to develop a time series forecasting model.\n",
    "The dataset used for the examples of this notebook is on air pollution measured by concentration of\n",
    "particulate matter (PM) of diameter less than or equal to 2.5 micrometers. There are other variables\n",
    "such as air pressure, air temparature, dewpoint and so on.\n",
    "Two time series models are developed - one on air pressure and the other on pm2.5.\n",
    "The dataset has been downloaded from UCI Machine Learning Repository.\n",
    "https://archive.ics.uci.edu/ml/datasets/Beijing+PM2.5+Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "import os\n",
    "import sys\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "import datetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#set current working directory\n",
    "os.chdir('D:/Practical Time Series')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Read the dataset into a pandas.DataFrame\n",
    "df = pd.read_csv('datasets/PRSA_data_2010.1.1-2014.12.31.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of the dataframe: (43824, 13)\n"
     ]
    }
   ],
   "source": [
    "print('Shape of the dataframe:', df.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>No</th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "      <th>day</th>\n",
       "      <th>hour</th>\n",
       "      <th>pm2.5</th>\n",
       "      <th>DEWP</th>\n",
       "      <th>TEMP</th>\n",
       "      <th>PRES</th>\n",
       "      <th>cbwd</th>\n",
       "      <th>Iws</th>\n",
       "      <th>Is</th>\n",
       "      <th>Ir</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-11.0</td>\n",
       "      <td>1021.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>1.79</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-12.0</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>4.92</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-11.0</td>\n",
       "      <td>1019.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>6.71</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-14.0</td>\n",
       "      <td>1019.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>9.84</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-20</td>\n",
       "      <td>-12.0</td>\n",
       "      <td>1018.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>12.97</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   No  year  month  day  hour  pm2.5  DEWP  TEMP    PRES cbwd    Iws  Is  Ir\n",
       "0   1  2010      1    1     0    NaN   -21 -11.0  1021.0   NW   1.79   0   0\n",
       "1   2  2010      1    1     1    NaN   -21 -12.0  1020.0   NW   4.92   0   0\n",
       "2   3  2010      1    1     2    NaN   -21 -11.0  1019.0   NW   6.71   0   0\n",
       "3   4  2010      1    1     3    NaN   -21 -14.0  1019.0   NW   9.84   0   0\n",
       "4   5  2010      1    1     4    NaN   -20 -12.0  1018.0   NW  12.97   0   0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Let's see the first five rows of the DataFrame\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make sure that the rows are in the right order of date and time of observations,\n",
    "a new column datetime is created from the date and time related columns of the DataFrame.\n",
    "The new column consists of Python's datetime.datetime objects. The DataFrame is sorted in ascending order\n",
    "over this column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df['datetime'] = df[['year', 'month', 'day', 'hour']].apply(lambda row: datetime.datetime(year=row['year'], month=row['month'], day=row['day'],\n",
    "                                                                                          hour=row['hour']), axis=1)\n",
    "df.sort_values('datetime', ascending=True, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x14d195fe2e8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TiCAA04ggANOIIADTiCAA04ggANOIIADTiCAA04ggANOIIADTiCAA04ggANOIIADTiCAA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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14d18fbe828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let us draw a box plot to visualize the central tendency and dispersion of PRES\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.boxplot(df['PRES'])\n",
    "g.set_title('Box plot of Air Pressure')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x14d1967d710>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mUAe+RGTFf749bLbNZ4wgmwr78OGGi3bq1AnvvPMORo0aBTe3psMHDBjAnxRO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\nYRDSsIUQwiD+Dytnv+RROjE6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14d195dceb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df['PRES'])\n",
    "g.set_title('Time series of Air Pressure')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('Air Pressure readings in hPa')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gradient descent algorithms perform better (for example converge faster) if the variables are wihtin range [-1, 1]. The PRES variable is minmax scaled as shown in the following cell in order to bound the scaled features within [0, 1]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import MinMaxScaler\n",
    "scaler = MinMaxScaler(feature_range=(0, 1))\n",
    "df['scaled_PRES'] = scaler.fit_transform(np.array(df['PRES']).reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Before training the model, the dataset is split in two parts - train set and validation set.\n",
    "The neural network is trained on the train set. This means computation of the loss function, back propagation\n",
    "and weights updated by a gradient descent algorithm is done on the train set. The validation set is\n",
    "used to evaluate the model and to determine the number of epochs in model training. Increasing the number of \n",
    "epochs will further decrease the loss function on the train set but might not neccesarily have the same effect\n",
    "for the validation set due to overfitting on the train set.Hence, the number of epochs is controlled by keeping\n",
    "a tap on the loss function computed for the validation set. We use Keras with Tensorflow backend to define and train\n",
    "the model. All the steps involved in model training and validation is done by calling appropriate functions\n",
    "of the Keras API."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of train: (35064, 15)\n",
      "Shape of test: (8760, 15)\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Let's start by splitting the dataset into train and validation. The dataset's time period if from\n",
    "Jan 1st, 2010 to Dec 31st, 2014. The first fours years - 2010 to 2013 is used as train and\n",
    "2014 is kept for validation.\n",
    "\"\"\"\n",
    "split_date = datetime.datetime(year=2014, month=1, day=1, hour=0)\n",
    "df_train = df.loc[df['datetime']<split_date]\n",
    "df_val = df.loc[df['datetime']>=split_date]\n",
    "print('Shape of train:', df_train.shape)\n",
    "print('Shape of test:', df_val.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>No</th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "      <th>day</th>\n",
       "      <th>hour</th>\n",
       "      <th>pm2.5</th>\n",
       "      <th>DEWP</th>\n",
       "      <th>TEMP</th>\n",
       "      <th>PRES</th>\n",
       "      <th>cbwd</th>\n",
       "      <th>Iws</th>\n",
       "      <th>Is</th>\n",
       "      <th>Ir</th>\n",
       "      <th>datetime</th>\n",
       "      <th>scaled_PRES</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-11.0</td>\n",
       "      <td>1021.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>1.79</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-01 00:00:00</td>\n",
       "      <td>0.545455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-12.0</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>4.92</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-01 01:00:00</td>\n",
       "      <td>0.527273</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-11.0</td>\n",
       "      <td>1019.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>6.71</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-01 02:00:00</td>\n",
       "      <td>0.509091</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-14.0</td>\n",
       "      <td>1019.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>9.84</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-01 03:00:00</td>\n",
       "      <td>0.509091</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-20</td>\n",
       "      <td>-12.0</td>\n",
       "      <td>1018.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>12.97</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-01 04:00:00</td>\n",
       "      <td>0.490909</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   No  year  month  day  hour  pm2.5  DEWP  TEMP    PRES cbwd    Iws  Is  Ir  \\\n",
       "0   1  2010      1    1     0    NaN   -21 -11.0  1021.0   NW   1.79   0   0   \n",
       "1   2  2010      1    1     1    NaN   -21 -12.0  1020.0   NW   4.92   0   0   \n",
       "2   3  2010      1    1     2    NaN   -21 -11.0  1019.0   NW   6.71   0   0   \n",
       "3   4  2010      1    1     3    NaN   -21 -14.0  1019.0   NW   9.84   0   0   \n",
       "4   5  2010      1    1     4    NaN   -20 -12.0  1018.0   NW  12.97   0   0   \n",
       "\n",
       "             datetime  scaled_PRES  \n",
       "0 2010-01-01 00:00:00     0.545455  \n",
       "1 2010-01-01 01:00:00     0.527273  \n",
       "2 2010-01-01 02:00:00     0.509091  \n",
       "3 2010-01-01 03:00:00     0.509091  \n",
       "4 2010-01-01 04:00:00     0.490909  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#First five rows of train\n",
    "df_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>No</th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "      <th>day</th>\n",
       "      <th>hour</th>\n",
       "      <th>pm2.5</th>\n",
       "      <th>DEWP</th>\n",
       "      <th>TEMP</th>\n",
       "      <th>PRES</th>\n",
       "      <th>cbwd</th>\n",
       "      <th>Iws</th>\n",
       "      <th>Is</th>\n",
       "      <th>Ir</th>\n",
       "      <th>datetime</th>\n",
       "      <th>scaled_PRES</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>35064</th>\n",
       "      <td>35065</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>-20</td>\n",
       "      <td>7.0</td>\n",
       "      <td>1014.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>143.48</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 00:00:00</td>\n",
       "      <td>0.418182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35065</th>\n",
       "      <td>35066</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>53.0</td>\n",
       "      <td>-20</td>\n",
       "      <td>7.0</td>\n",
       "      <td>1013.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>147.50</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 01:00:00</td>\n",
       "      <td>0.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35066</th>\n",
       "      <td>35067</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>65.0</td>\n",
       "      <td>-20</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1013.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>151.52</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 02:00:00</td>\n",
       "      <td>0.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35067</th>\n",
       "      <td>35068</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>70.0</td>\n",
       "      <td>-20</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1013.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>153.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 03:00:00</td>\n",
       "      <td>0.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35068</th>\n",
       "      <td>35069</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>79.0</td>\n",
       "      <td>-18</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1012.0</td>\n",
       "      <td>cv</td>\n",
       "      <td>0.89</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 04:00:00</td>\n",
       "      <td>0.381818</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          No  year  month  day  hour  pm2.5  DEWP  TEMP    PRES cbwd     Iws  \\\n",
       "35064  35065  2014      1    1     0   24.0   -20   7.0  1014.0   NW  143.48   \n",
       "35065  35066  2014      1    1     1   53.0   -20   7.0  1013.0   NW  147.50   \n",
       "35066  35067  2014      1    1     2   65.0   -20   6.0  1013.0   NW  151.52   \n",
       "35067  35068  2014      1    1     3   70.0   -20   6.0  1013.0   NW  153.31   \n",
       "35068  35069  2014      1    1     4   79.0   -18   3.0  1012.0   cv    0.89   \n",
       "\n",
       "       Is  Ir            datetime  scaled_PRES  \n",
       "35064   0   0 2014-01-01 00:00:00     0.418182  \n",
       "35065   0   0 2014-01-01 01:00:00     0.400000  \n",
       "35066   0   0 2014-01-01 02:00:00     0.400000  \n",
       "35067   0   0 2014-01-01 03:00:00     0.400000  \n",
       "35068   0   0 2014-01-01 04:00:00     0.381818  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#First five rows of validation\n",
    "df_val.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Reset the indices of the validation set\n",
    "df_val.reset_index(drop=True, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x14d19ac5fd0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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thF89lbEEZ82ahbNnz+LFF1+ESqVCjx490KpVK8ENY4s3R+K20DlRMMcA2ZtW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\nAZ9+WoTmzZ3P5/p6JH7kSD4mTy5Cy5aGsuPbh/yEmSAsON9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rkZOTA09PT4wdOxY5OTnQ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\nYxEnIlKw/wP0dQ0qCJgifAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14d19898390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GjRuHpUuXwmaz4ZprrsFff/2lqLNq1aqYOXMmpk2bhpKSEhBCMG3aNNSqVQt9+vTBsWPH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\nIAwCCTJBEIRBIEEmCIIwCP8fLKHqOQ/k0jEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14d19aaca58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "The train and validation time series of standardized PRES is also plotted.\n",
    "\"\"\"\n",
    "\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df_train['scaled_PRES'], color='b')\n",
    "g.set_title('Time series of scaled Air Pressure in train set')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('Scaled Air Pressure readings')\n",
    "\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df_val['scaled_PRES'], color='r')\n",
    "g.set_title('Time series of scaled Air Pressure in validation set')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('Scaled Air Pressure readings')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to generate regressors (X) and target variable (y) for train and validation. 2-D array of regressor and 1-D array of target is created from the original 1-D array of columm scaled_PRES in the DataFrames. For the time series forecasting model, Past seven days of observations are used to predict for the next day. This is equivalent to a AR(7) model. We define a function which takes the original time series and the number of timesteps in regressors as input to generate the arrays of X and y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def makeXy(ts, nb_timesteps):\n",
    "    \"\"\"\n",
    "    Input: \n",
    "           ts: original time series\n",
    "           nb_timesteps: number of time steps in the regressors\n",
    "    Output: \n",
    "           X: 2-D array of regressors\n",
    "           y: 1-D array of target \n",
    "    \"\"\"\n",
    "    X = []\n",
    "    y = []\n",
    "    for i in range(nb_timesteps, ts.shape[0]):\n",
    "        X.append(list(ts.loc[i-nb_timesteps:i-1]))\n",
    "        y.append(ts.loc[i])\n",
    "    X, y = np.array(X), np.array(y)\n",
    "    return X, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of train arrays: (35057, 7) (35057,)\n"
     ]
    }
   ],
   "source": [
    "X_train, y_train = makeXy(df_train['scaled_PRES'], 7)\n",
    "print('Shape of train arrays:', X_train.shape, y_train.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of validation arrays: (8753, 7) (8753,)\n"
     ]
    }
   ],
   "source": [
    "X_val, y_val = makeXy(df_val['scaled_PRES'], 7)\n",
    "print('Shape of validation arrays:', X_val.shape, y_val.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The input to RNN layers must be of shape (number of samples, number of timesteps, number of features per timestep). In this case we are modeling only pm2.5 hence number of features per timestep is one. Number of timesteps is seven and number of samples is same as the number of samples in X_train and X_val, which are reshaped to 3D arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of 3D arrays: (35057, 7, 1) (8753, 7, 1)\n"
     ]
    }
   ],
   "source": [
    "X_train, X_val = X_train.reshape((X_train.shape[0], X_train.shape[1], 1)), X_val.reshape((X_val.shape[0], X_val.shape[1], 1))\n",
    "print('Shape of 3D arrays:', X_train.shape, X_val.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we define the MLP using the Keras Functional API. In this approach a layer can be declared as the input of the following layer at the time of defining the next layer. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from keras.layers import Dense, Input, Dropout\n",
    "from keras.layers.recurrent import GRU\n",
    "from keras.optimizers import SGD\n",
    "from keras.models import Model\n",
    "from keras.models import load_model\n",
    "from keras.callbacks import ModelCheckpoint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Define input layer which has shape (None, 7) and of type float32. None indicates the number of instances\n",
    "input_layer = Input(shape=(7,1), dtype='float32')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#LSTM layer is defined for seven timesteps\n",
    "gru_layer = GRU(64, input_shape=(7,1), return_sequences=False)(input_layer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dropout_layer = Dropout(0.2)(gru_layer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Finally the output layer gives prediction for the next day's air pressure.\n",
    "output_layer = Dense(1, activation='linear')(dropout_layer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The input, dense and output layers will now be packed inside a Model, which is wrapper class for training and making\n",
    "predictions. Mean square error (mse) is used as the loss function.\n",
    "\n",
    "The network's weights are optimized by the Adam algorithm. Adam stands for adaptive moment estimation\n",
    "and has been a popular choice for training deep neural networks. Unlike, stochastic gradient descent, adam uses\n",
    "different learning rates for each weight and separately updates the same as the training progresses. The learning rate of a weight is updated based on exponentially weighted moving averages of the weight's gradients and the squared gradients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_1 (InputLayer)         (None, 7, 1)              0         \n",
      "_________________________________________________________________\n",
      "gru_1 (GRU)                  (None, 64)                12672     \n",
      "_________________________________________________________________\n",
      "dropout_1 (Dropout)          (None, 64)                0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 1)                 65        \n",
      "=================================================================\n",
      "Total params: 12,737\n",
      "Trainable params: 12,737\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "ts_model = Model(inputs=input_layer, outputs=output_layer)\n",
    "ts_model.compile(loss='mse', optimizer='adam')\n",
    "ts_model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 35057 samples, validate on 8753 samples\n",
      "Epoch 1/20\n",
      "35057/35057 [==============================] - 16s - loss: 0.0020 - val_loss: 3.3810e-04\n",
      "Epoch 2/20\n",
      "35057/35057 [==============================] - 23s - loss: 6.2747e-04 - val_loss: 1.4782e-04\n",
      "Epoch 3/20\n",
      "35057/35057 [==============================] - 19s - loss: 3.9528e-04 - val_loss: 1.5410e-04\n",
      "Epoch 4/20\n",
      "35057/35057 [==============================] - 12s - loss: 3.2953e-04 - val_loss: 1.4294e-04\n",
      "Epoch 5/20\n",
      "35057/35057 [==============================] - 13s - loss: 3.1658e-04 - val_loss: 1.4473e-04\n",
      "Epoch 6/20\n",
      "35057/35057 [==============================] - 11s - loss: 3.1082e-04 - val_loss: 1.4149e-04\n",
      "Epoch 7/20\n",
      "35057/35057 [==============================] - 12s - loss: 3.0778e-04 - val_loss: 2.3025e-04\n",
      "Epoch 8/20\n",
      "35057/35057 [==============================] - 12s - loss: 3.1214e-04 - val_loss: 1.6912e-04\n",
      "Epoch 9/20\n",
      "35057/35057 [==============================] - 12s - loss: 3.0986e-04 - val_loss: 1.4575e-04\n",
      "Epoch 10/20\n",
      "35057/35057 [==============================] - 11s - loss: 3.0881e-04 - val_loss: 1.4396e-04\n",
      "Epoch 11/20\n",
      "35057/35057 [==============================] - 11s - loss: 3.0886e-04 - val_loss: 1.3504e-04\n",
      "Epoch 12/20\n",
      "35057/35057 [==============================] - 11s - loss: 3.0070e-04 - val_loss: 1.4724e-04\n",
      "Epoch 13/20\n",
      "35057/35057 [==============================] - 12s - loss: 3.0694e-04 - val_loss: 1.5815e-04\n",
      "Epoch 14/20\n",
      "35057/35057 [==============================] - 11s - loss: 3.0676e-04 - val_loss: 1.3675e-04\n",
      "Epoch 15/20\n",
      "35057/35057 [==============================] - 11s - loss: 3.0573e-04 - val_loss: 1.4789e-04\n",
      "Epoch 16/20\n",
      "35057/35057 [==============================] - 11s - loss: 3.0122e-04 - val_loss: 1.4200e-04\n",
      "Epoch 17/20\n",
      "35057/35057 [==============================] - 12s - loss: 3.0389e-04 - val_loss: 1.3398e-04\n",
      "Epoch 18/20\n",
      "35057/35057 [==============================] - 12s - loss: 3.0106e-04 - val_loss: 1.3336e-04\n",
      "Epoch 19/20\n",
      "35057/35057 [==============================] - 11s - loss: 3.0345e-04 - val_loss: 1.6434e-04\n",
      "Epoch 20/20\n",
      "35057/35057 [==============================] - 11s - loss: 3.0174e-04 - val_loss: 2.1796e-04\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x14d838ce780>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "The model is trained by calling the fit function on the model object and passing the X_train and y_train. The training \n",
    "is done for a predefined number of epochs. Additionally, batch_size defines the number of samples of train set to be\n",
    "used for a instance of back propagation.The validation dataset is also passed to evaluate the model after every epoch\n",
    "completes. A ModelCheckpoint object tracks the loss function on the validation set and saves the model for the epoch,\n",
    "at which the loss function has been minimum.\n",
    "\"\"\"\n",
    "save_weights_at = os.path.join('keras_models', 'PRSA_data_Air_Pressure_GRU_weights.{epoch:02d}-{val_loss:.4f}.hdf5')\n",
    "save_best = ModelCheckpoint(save_weights_at, monitor='val_loss', verbose=0,\n",
    "                            save_best_only=True, save_weights_only=False, mode='min',\n",
    "                            period=1)\n",
    "ts_model.fit(x=X_train, y=y_train, batch_size=16, epochs=20,\n",
    "             verbose=1, callbacks=[save_best], validation_data=(X_val, y_val),\n",
    "             shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prediction are made for the air pressure from the best saved model. The model's predictions, which are on the minmax scaled  air-pressure, are inverse transformed to get predictions on original air pressure. The goodness-of-fit, R-squared is also calculated for the predictions on the original variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "best_model = load_model(os.path.join('keras_models', 'PRSA_data_Air_Pressure_GRU_weights.17-0.0001.hdf5'))\n",
    "preds = best_model.predict(X_val)\n",
    "pred_PRES = scaler.inverse_transform(preds)\n",
    "pred_PRES = np.squeeze(pred_PRES)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R-squared on validation set of the original air pressure: 0.995799194476\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "r2 = r2_score(df_val['PRES'].loc[7:], pred_PRES)\n",
    "print('R-squared on validation set of the original air pressure:', r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x14d84a7e4e0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KYEiIx5AQX6p978Ld3B2r8NRT3qSnSzz3XD6JiTns+Og31ryVwIcf5tKggcpH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\n8rNyMQsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14d84a6feb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let's plot the first 50 actual and predicted values of air pressure.\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "plt.plot(range(50), df_val['PRES'].loc[7:56], linestyle='-', marker='*', color='r')\n",
    "plt.plot(range(50), pred_PRES[:50], linestyle='-', marker='.', color='b')\n",
    "plt.legend(['Actual','Predicted'], loc=2)\n",
    "plt.title('Actual vs Predicted Air Pressure')\n",
    "plt.ylabel('Air Pressure')\n",
    "plt.xlabel('Index')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
